Responding to the former Conservative chairman's controversial remarks, Mr Adams said it was unacceptable for a member of the House of the Lords to openly support the shooting of a political leader.

"I fully understand that Norman Tebbit has himself been a victim of the political conflict and I regret that he has suffered grievously," said Mr Adams, a former West Belfast MP and now TD for Louth in the Irish parliament.

"However, to publicly advocate the assassination of Deputy First Minister Martin McGuinness is a shocking throwback to a violent past from which we are seeking to move on."

Mr Adams said his party colleague and ex-IRA commander Mr McGuinness has worked tirelessly to ensure the success of the peace process at considerable risk to himself.

"Martin, his home and indeed his family have been targets for abuse and attack by so-called dissident republicans," he said.

"To now have this type of activity encouraged by a member of the British House of Lords is unacceptable, and should be rejected by all right thinking people.

"Political leaders on both sides of the Irish Sea should reject the sentiments expressed by Mr Tebbitt."

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Outspoken Lord Tebbit, who was injured with his wife during the 1984 IRA bombing of the Grand Hotel in Brighton, said he hoped Mr McGuinness is shot in the back for attending a State banquet at the invitation of the Queen.

Mr McGuinness said the remarks were "not fitting" for someone who holds high political office.

"Obviously the sentiments that he has expressed, I think, are not fitting for someone in the elected position he has been in for a very long time," he said.

But he insisted he would not be drawn into a row over the comments.

"I'm not going to make an issue of it," he said.

"Other people have certainly raised it with me, and some people have advocated that I should make an issue of it - I don't intend to do so."

Lord Tebbit said the Queen had no choice about Mr McGuinness attending the State banquet at Windsor Castle last night in honour of the visit of Irish President Michael D Higgins - the first time an Irish head of state has been officially invited to Britain.

Lord Tebbit was injured with his wife during the 1984 IRA bombing of the Grand Hotel in Brighton [AP]

He said: "There's always the possibility that a member of the Real IRA will be so outraged by Mr McGuinness bowing to the Queen that they might shoot him in the back for it.

"We can but hope."

Mr McGuinness said he had no qualms about standing and joining in a toast to the Queen, the Duke of Edinburgh and the people of the UK as an orchestra played God Save The Queen during the dinner.

"I went to Windsor Castle last night as an unapologetic Irish republican, and I'm still an unapologetic Irish republican this morning," he said.

"So I think it is possible to do these things, particularly in the context of a very clear indicator that others - such as Queen Elizabeth in her visit to our country, both to Belfast and to the south - were prepared to show impressive leadership in the context of conflict resolution and acts of reconciliation."

He added: "I believe I have the overwhelming support of the people of Ireland for what I did last night."

Mr McGuinness said he understood the pain of people affected by the Troubles and defended their right to protest at his attendance.

Martin McGuinness attending the State banquet at Windsor Castle last night [AP]

"I understand that people are hurting as a result of the fall-out from the conflict and many in my community - in the republican, nationalist community - are also hurting as a result of the conflict," he said.

"Different sections of that community come to this at different speeds."

The former MP, who refused to sit in the House of Commons because of the oath to the Queen and who snubbed her ground-breaking visit to Ireland in 2011, also berated Prime Minister David Cameron over inaction in the Irish peace process.

"I had a word with David Cameron during the course of the event last night and told him that the British Government bears a huge responsibility in terms of moving this process forward," he said.

"It is a responsibility they have not taken up in the course of recent times.

"And I said to him that I think it is vitally important that he has the same hands-on approach to resolving the outstanding issues as had the previous Labour administration."